RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-03_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 14.0040 0.333181 2 to 25 15.68 12.0699 0.204116 3 to 26 15.57 27.9043 0.953931 4 to 27 15.49 13.7089 0.312408 5 to 28 15.59 22.9025 0.847547 6 to 29 15.63 18.9641 0.669402 7 to 30 15.78 33.5608 0.990438 8 to 31 15.78 18.1307 0.619357 9 to 32 15.80 15.7093 0.455469 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.420393 Tough bday spacings test for dh-ranFile-2018-04-03_11:31: 4096 birthdays, year=2^32 days Table of Expected vs. Observed counts: Duplicates 0 1 2 3 4 5 6 7 8 9 >=10 Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1 Observed 8 38 70 88 107 83 47 31 16 8 4 (O-E)^2/E 0.1 0.1 0.1 1.0 0.9 0.3 0.5 0.1 0.1 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 3.417, p= 0.030 RESULTS OF GCD FOR dh-ranFile-2018-04-03_11:31 Euclid's algorithm: p-value, steps to gcd: 0.089622 p-value, dist. of gcd's: 0.324432 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-03_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.039 0.672 0.084 0.715 0.201 0.567 0.460 0.822 Bits 8 to 15---> 0.667 0.759 0.194 0.575 0.537 0.537 0.648 0.899 Bits 16 to 23---> 0.392 0.825 0.607 0.164 0.362 0.326 0.294 0.550 Bits 24 to 31---> 0.071 0.509 0.690 0.077 0.601 0.687 0.574 0.891 KS test for the above 32 p values: 0.581 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-03_11:31, p-values for 5 runs: 0.5882, 0.9081, 0.4261, 0.4948, 0.3538 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-03_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 233 211.4 2.203 2.203 r= 29 5033 5134.0 1.987 4.190 r= 30 23271 23103.0 1.221 5.411 r= 31 11463 11551.5 0.678 6.090 chi-square = 6.090 with df = 3; p-value = 0.893 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-03_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 196 211.4 1.124 1.124 r= 30 5264 5134.0 3.291 4.416 r= 31 22994 23103.0 0.515 4.930 r= 32 11546 11551.5 0.003 4.933 chi-square = 4.933 with df = 3; p-value = 0.823 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-03_11:31 b-rank test for bits 1 to 8, p=0.21370 b-rank test for bits 2 to 9, p=0.52669 b-rank test for bits 3 to 10, p=0.44366 b-rank test for bits 4 to 11, p=0.58593 b-rank test for bits 5 to 12, p=0.28458 b-rank test for bits 6 to 13, p=0.26017 b-rank test for bits 7 to 14, p=0.62390 b-rank test for bits 8 to 15, p=0.90713 b-rank test for bits 9 to 16, p=0.11266 b-rank test for bits 10 to 17, p=0.02809 b-rank test for bits 11 to 18, p=0.43397 b-rank test for bits 12 to 19, p=0.12744 b-rank test for bits 13 to 20, p=0.86744 b-rank test for bits 14 to 21, p=0.65502 b-rank test for bits 15 to 22, p=0.13377 b-rank test for bits 16 to 23, p=0.77020 b-rank test for bits 17 to 24, p=0.35496 b-rank test for bits 18 to 25, p=0.65494 b-rank test for bits 19 to 26, p=0.49349 b-rank test for bits 20 to 27, p=0.43101 b-rank test for bits 21 to 28, p=0.86606 b-rank test for bits 22 to 29, p=0.44173 b-rank test for bits 23 to 30, p=0.42973 b-rank test for bits 24 to 31, p=0.81736 b-rank test for bits 25 to 32, p=0.40781 TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices The above should be 25 uniform [0,1] random variables: The KS test for those 25 supposed UNI's yields p = 0.645632 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-03_11:31 (20 bits/word, 2097152 words 20 bitstreams. No. missing words should average 141909.33 with sigma=428.00.) ---------------------------------------------------------------- BITSTREAM test results. Bitstream No. missing words z-score p-value 1 141684 -0.53 0.299280 2 141164 -1.74 0.040805 3 141971 0.14 0.557285 4 141761 -0.35 0.364459 5 142796 2.07 0.980851 6 142458 1.28 0.900068 7 141940 0.07 0.528563 8 142278 0.86 0.805485 9 142224 0.74 0.768894 10 142211 0.70 0.759544 11 141728 -0.42 0.335904 12 141942 0.08 0.530422 13 142495 1.37 0.914405 14 141391 -1.21 0.112938 15 142376 1.09 0.862221 16 141585 -0.76 0.224291 17 142102 0.45 0.673704 18 141858 -0.12 0.452269 19 142245 0.78 0.783561 20 141713 -0.46 0.323219 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-03_11:31 Bits used No. missing words z-score p-value 23 to 32 142219 1.0678 0.857201 22 to 31 142438 1.8230 0.965848 21 to 30 141473 -1.5046 0.066215 20 to 29 141643 -0.9184 0.179210 19 to 28 141921 0.0402 0.516050 18 to 27 142019 0.3782 0.647349 17 to 26 141757 -0.5253 0.299696 16 to 25 141969 0.2058 0.581510 15 to 24 142117 0.7161 0.763036 14 to 23 142259 1.2058 0.886045 13 to 22 142127 0.7506 0.773549 12 to 21 142232 1.1127 0.867072 11 to 20 141328 -2.0046 0.022504 10 to 19 141612 -1.0253 0.152617 9 to 18 141984 0.2575 0.601597 8 to 17 141864 -0.1563 0.437894 7 to 16 141199 -2.4494 0.007154 6 to 15 141768 -0.4873 0.313007 5 to 14 142102 0.6644 0.746776 4 to 13 142005 0.3299 0.629261 3 to 12 141564 -1.1908 0.116867 2 to 11 141755 -0.5322 0.297303 1 to 10 142393 1.6678 0.952325 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-03_11:31 Bits used No. missing words z-score p-value 28 to 32 142266 1.2091 0.886678 27 to 31 141798 -0.3774 0.352942 26 to 30 142198 0.9785 0.836097 25 to 29 142225 1.0701 0.857706 24 to 28 141880 -0.0994 0.460401 23 to 27 142565 2.2226 0.986879 22 to 26 142491 1.9718 0.975682 21 to 25 141863 -0.1571 0.437602 20 to 24 141825 -0.2859 0.387491 19 to 23 142127 0.7379 0.769702 18 to 22 141423 -1.6486 0.049617 17 to 21 142065 0.5277 0.701145 16 to 20 142190 0.9514 0.829305 15 to 19 141293 -2.0893 0.018342 14 to 18 141503 -1.3774 0.084196 13 to 17 141621 -0.9774 0.164188 12 to 16 142003 0.3175 0.624578 11 to 15 142008 0.3345 0.630989 10 to 14 141653 -0.8689 0.192447 9 to 13 141969 0.2023 0.580148 8 to 12 141986 0.2599 0.602529 7 to 11 142012 0.3480 0.636093 6 to 10 142246 1.1413 0.873118 5 to 9 141913 0.0124 0.504963 4 to 8 141756 -0.5198 0.301615 3 to 7 142037 0.4328 0.667413 2 to 6 141453 -1.5469 0.060946 1 to 5 141988 0.2667 0.605141 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-03_11:31 Bits used No. missing words z-score p-value 31 to 32 141735 -0.5142 0.303539 30 to 31 142212 0.8928 0.814026 29 to 30 141742 -0.4936 0.310795 28 to 29 141638 -0.8004 0.211744 27 to 28 141712 -0.5821 0.280252 26 to 27 141548 -1.0659 0.143241 25 to 26 141458 -1.3314 0.091536 24 to 25 141639 -0.7974 0.212600 23 to 24 141692 -0.6411 0.260732 22 to 23 142162 0.7453 0.771967 21 to 22 141538 -1.0954 0.136678 20 to 21 142151 0.7129 0.762043 19 to 20 142029 0.3530 0.637959 18 to 19 142414 1.4887 0.931717 17 to 18 142212 0.8928 0.814026 16 to 17 141412 -1.4671 0.071181 15 to 16 141565 -1.0157 0.154881 14 to 15 141664 -0.7237 0.234629 13 to 14 141517 -1.1573 0.123572 12 to 13 141404 -1.4906 0.068027 11 to 12 141436 -1.3963 0.081319 10 to 11 141490 -1.2370 0.108051 9 to 10 141604 -0.9007 0.183880 8 to 9 141776 -0.3933 0.347048 7 to 8 142008 0.2911 0.614498 6 to 7 141743 -0.4906 0.311837 5 to 6 141614 -0.8712 0.191828 4 to 5 142153 0.7188 0.763865 3 to 4 141879 -0.0895 0.464355 2 to 3 141940 0.0905 0.536044 1 to 2 142152 0.7158 0.762955 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-03_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2502.16 0.031 0.512183 Test results for specific bytes for dh-ranFile-2018-04-03_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2449.02 -0.721 0.235445 2 to 9 2550.93 0.720 0.764296 3 to 10 2435.94 -0.906 0.182487 4 to 11 2349.78 -2.124 0.016818 5 to 12 2573.76 1.043 0.851556 6 to 13 2509.84 0.139 0.555355 7 to 14 2524.24 0.343 0.634107 8 to 15 2536.09 0.510 0.695103 9 to 16 2491.98 -0.113 0.454836 10 to 17 2449.86 -0.709 0.239122 11 to 18 2493.19 -0.096 0.461612 12 to 19 2424.17 -1.072 0.141770 13 to 20 2518.62 0.263 0.603855 14 to 21 2500.04 0.001 0.500239 15 to 22 2487.12 -0.182 0.427733 16 to 23 2417.43 -1.168 0.121470 17 to 24 2512.41 0.176 0.569686 18 to 25 2487.66 -0.174 0.430744 19 to 26 2481.28 -0.265 0.395606 20 to 27 2494.22 -0.082 0.467399 21 to 28 2584.50 1.195 0.883971 22 to 29 2621.96 1.725 0.957712 23 to 30 2469.46 -0.432 0.332914 24 to 31 2509.98 0.141 0.556116 25 to 32 2501.84 0.026 0.510385 CDPARK for dh-ranFile-2018-04-03_11:31: result of 10 tests (Of 12000 tries, the average no. of successes should be 3523.0 with sigma=21.9) No. succeses z-score p-value 3516 -0.3196 0.374623 3506 -0.7763 0.218799 3488 -1.5982 0.055002 3512 -0.5023 0.307734 3532 0.4110 0.659449 3475 -2.1918 0.014198 3545 1.0046 0.842447 3505 -0.8219 0.205562 3524 0.0457 0.518210 3516 -0.3196 0.374623 Square side=100, avg. no. parked=3511.90 sample std.=19.22 p-value of the KSTEST for those 10 p-values: 0.200728 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-03_11:31 0.8130,0.9479,0.6729,0.4845,0.1133,0.2631,0.1873,0.5786,0.4140,0.0075, The KS test for those 10 p-values: 0.907256 The 3DSPHERES test for dh-ranFile-2018-04-03_11:31 sample no r^3 equiv. uni. 1 7.094 0.210599 2 15.512 0.403736 3 1.678 0.054385 4 26.610 0.588115 5 38.381 0.721784 6 1.906 0.061558 7 126.234 0.985121 8 1.153 0.037694 9 65.550 0.887522 10 3.412 0.107517 11 5.866 0.177600 12 64.291 0.882703 13 20.571 0.496264 14 5.730 0.173866 15 55.568 0.843118 16 5.243 0.160342 17 45.531 0.780781 18 7.257 0.214874 19 37.519 0.713675 20 6.537 0.195801 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.257410 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-03_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -1.8 0.8 -1.4 2.0 0.0 2.1 -1.1 -1.0 0.1 -0.1 -0.6 -0.5 0.4 -0.4 0.4 0.6 1.3 -0.6 -1.4 -0.8 0.2 -0.5 -0.1 2.5 1.0 -1.2 0.6 0.2 -0.1 -0.1 0.6 -0.3 -1.5 1.3 0.3 0.2 -0.8 -0.1 -0.6 0.0 1.8 Chi-square with 42 degrees of freedom:40.739173 z-score=-0.137567, p-value=0.473703 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-03_11:31 Test no p-value 1 0.184287 2 0.450846 3 0.022573 4 0.004622 5 0.914060 6 0.212809 7 0.456899 8 0.036842 9 0.307208 10 0.706090 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.051192 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-03_11:31: (for k>=2, the prob. of a run of length k is 2*k/(k+1)!) Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E 2 66666.67 66802 0.27 66594 0.08 3 25000.00 24845 0.96 24961 0.06 4 6666.67 6654 0.02 6774 1.73 5 1388.89 1421 0.74 1389 0.00 6 238.10 236 0.02 243 0.10 7 34.72 36 0.05 35 0.00 8 4.96 5 0.00 3 0.77 p=0.08667 p=0.16000 Number of rngs required: 687453, p-value: 0.135 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-03_11:31 No. of wins: Observed Expected 98455 98585.9 z-score=-0.585, pvalue=0.27918 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66711 66666.7 0.029 0.029 2 37634 37654.3 0.011 0.040 3 26968 26954.7 0.007 0.047 4 19020 19313.5 4.459 4.506 5 13974 13851.4 1.085 5.591 6 9887 9943.5 0.322 5.912 7 7255 7145.0 1.693 7.605 8 5100 5139.1 0.297 7.902 9 3677 3699.9 0.141 8.043 10 2687 2666.3 0.161 8.204 11 1975 1923.3 1.388 9.592 12 1380 1388.7 0.055 9.647 13 994 1003.7 0.094 9.741 14 769 726.1 2.530 12.271 15 525 525.8 0.001 12.272 16 396 381.2 0.579 12.851 17 288 276.5 0.475 13.326 18 205 200.8 0.087 13.412 19 155 146.0 0.557 13.969 20 103 106.2 0.097 14.067 21 297 287.1 0.340 14.407 Chisq= 14.41 for 20 degrees of freedom, p= 0.19072 SUMMARY of craptest p-value for no. of wins: 0.279181 p-value for throws/game: 0.190724 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-03_11:31 No. of wins: Observed Expected 98593 98585.9 z-score= 0.032, pvalue=0.51274 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66563 66666.7 0.161 0.161 2 37419 37654.3 1.471 1.632 3 27352 26954.7 5.855 7.487 4 19277 19313.5 0.069 7.556 5 13798 13851.4 0.206 7.762 6 9986 9943.5 0.181 7.943 7 7037 7145.0 1.633 9.576 8 5209 5139.1 0.952 10.528 9 3719 3699.9 0.099 10.627 10 2664 2666.3 0.002 10.629 11 1902 1923.3 0.237 10.865 12 1418 1388.7 0.616 11.482 13 1006 1003.7 0.005 11.487 14 724 726.1 0.006 11.493 15 502 525.8 1.080 12.574 16 384 381.2 0.021 12.595 17 280 276.5 0.043 12.638 18 216 200.8 1.146 13.784 19 152 146.0 0.248 14.032 20 86 106.2 3.847 17.880 21 306 287.1 1.242 19.122 Chisq= 19.12 for 20 degrees of freedom, p= 0.48608 SUMMARY of craptest p-value for no. of wins: 0.512740 p-value for throws/game: 0.486081 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0046,0.0072,0.0075,0.0142,0.0168,0.0183,0.0225,0.0226,0.0281,0.0301, 0.0368,0.0377,0.0386,0.0408,0.0496,0.0512,0.0544,0.0550,0.0609,0.0616, 0.0662,0.0680,0.0712,0.0714,0.0770,0.0813,0.0836,0.0842,0.0867,0.0896, 0.0915,0.1075,0.1081,0.1127,0.1129,0.1133,0.1169,0.1215,0.1236,0.1274, 0.1338,0.1352,0.1367,0.1418,0.1432,0.1526,0.1549,0.1600,0.1603,0.1635, 0.1642,0.1739,0.1776,0.1792,0.1825,0.1839,0.1843,0.1873,0.1907,0.1918, 0.1924,0.1939,0.1958,0.2007,0.2013,0.2041,0.2056,0.2106,0.2117,0.2126, 0.2128,0.2137,0.2149,0.2188,0.2243,0.2346,0.2354,0.2391,0.2574,0.2602, 0.2607,0.2631,0.2792,0.2803,0.2846,0.2935,0.2973,0.2993,0.2997,0.3016, 0.3035,0.3072,0.3077,0.3108,0.3118,0.3124,0.3130,0.3232,0.3244,0.3262, 0.3329,0.3332,0.3359,0.3470,0.3529,0.3538,0.3550,0.3620,0.3645,0.3746, 0.3746,0.3875,0.3923,0.3956,0.4037,0.4078,0.4140,0.4204,0.4261,0.4277, 0.4297,0.4307,0.4310,0.4340,0.4376,0.4379,0.4417,0.4437,0.4508,0.4523, 0.4548,0.4555,0.4569,0.4597,0.4604,0.4616,0.4644,0.4674,0.4737,0.4845, 0.4861,0.4935,0.4948,0.4963,0.5002,0.5050,0.5088,0.5104,0.5122,0.5127, 0.5160,0.5182,0.5267,0.5286,0.5304,0.5360,0.5368,0.5369,0.5502,0.5554, 0.5561,0.5573,0.5672,0.5697,0.5740,0.5748,0.5786,0.5801,0.5815,0.5815, 0.5859,0.5881,0.5882,0.6011,0.6016,0.6025,0.6039,0.6051,0.6070,0.6145, 0.6194,0.6239,0.6246,0.6293,0.6310,0.6341,0.6361,0.6380,0.6456,0.6473, 0.6484,0.6549,0.6550,0.6594,0.6668,0.6674,0.6694,0.6717,0.6729,0.6737, 0.6873,0.6895,0.6951,0.7011,0.7061,0.7137,0.7146,0.7218,0.7468,0.7586, 0.7595,0.7620,0.7630,0.7630,0.7639,0.7643,0.7689,0.7697,0.7702,0.7720, 0.7735,0.7808,0.7836,0.8055,0.8130,0.8140,0.8140,0.8174,0.8222,0.8232, 0.8254,0.8293,0.8361,0.8424,0.8431,0.8475,0.8516,0.8572,0.8577,0.8622, 0.8661,0.8671,0.8674,0.8731,0.8827,0.8840,0.8860,0.8867,0.8875,0.8909, 0.8927,0.8992,0.9001,0.9071,0.9073,0.9081,0.9141,0.9144,0.9317,0.9479, 0.9523,0.9539,0.9577,0.9658,0.9757,0.9809,0.9851,0.9869,0.9904, Overall p-value after applying KStest on 269 p-values = 0.098422 In response to requests, we have provided a list of all the p-values produced by the tests you have chosen for this run. The individual p-values are supposed to be uniform in [0,1), but they are not necessarily independent. So even though we have applied a KSTEST to the accumulated p-values, the result is not necessarily---even if your file contains truly random bits---uniform in [0,1). But it is probably pretty close, so take that last p-value with a grain of salt. In particular, there may be some values so close to 0 or 1 that the tests they came from should be applied several more times, or new, related tests should be undertaken.